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Review for Single Electron Transistor

Ling Yang

Abstract Single electron transistor (SET) is a novel idea and has been intensivelystudied. This review gives a general picture of SET, such as its mechanism, fabrication,application and problems faced.Key words SET quantum dot tunneling Chemical self-assembly

During 1980s, the main discoveries in mesoscopic physics are the tunneling of singleelectron and Coulomb blockade phenomena[1,2,13], which make many scientists predictthat if the size of the quantum dots is reduced to several nanometers, it is highly possibleto produce applicable single electron transistor (SET) which works above liquid nitrogentemperature, and this will bring a revolution to electronic science. Since then SET hasbeen a hot research area. The breakthrough of nanotech as well as its successfulcombination with semiconductor technologies gives hope to SET, and some think that itwill be a mature technique in the coming decade.

1 Mechanism of SETUsually electrons move continuously in the common transistors, but as the size of thesystem goes down to nanoscale (for example, the size of metal atoms can be several nm,and the size of semi-conductive particles can be several tens nm), the energy of thesystem is quantumized, that is, the process of charging and discharging is discontinuous.The energy for one electron to move into the system is:

CeEc 2/2=where C is the capacitance of this system. This Ec is called Coulomb blockade energy,which is the repelling energy of the previous electron to the next electron. For a tinysystem, the capacitance C is very small, thus Ec can be very high, and the electronscannot move simultaneously, but must pass through one by one. This phenomenon iscalled "Coulomb blockade", and has been observed in 1980s.

If two quantum dots(QD) are joined at a point and form a channel, it is possible for anelectron to pass from one dot over the energy barrier and move to the other dot, this iscalled "tunneling phenomenon". In order to overcome the barrier (Ec), the appliedvoltage on the quantum dots (V/2) should be

V > e/CIn order to observe Coulomb blockade and tunneling, the energy an electron assumesmust be higher than the thermal scattering energy, that is

TkCe B>2/2

where Bk is the Boltzman constant.As this equation predicts, if the capacitance is low enough, that is, if the size of the QDscan be reduced to several nm, Coulomb blockade and tunneling can be observed at high(room) temperature.If the two QDs are joined respectively with other conductive materials such as metalwires or conductive polymer leads, a SET is formed. A model of SET is shown in Fig.1,(b) is the simplified model. The two areas filled with patched pattern are tunneling

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junctions; there are some discrete Coulomb islands between them. R1, C1 and R2, C2 arethe resistance and capacitance of the junctions. The junctions form the source and drainof the transistor, 2/V± voltages are applied to them through conductive wires, thetunneling current pass through the islands is I. A layer of insulating media separates theislands from the gate; the capacitance between them is Cg. A voltage of Vg is applied onthe gate and controls the open or close of the SET.Because of its unique structure, SET has many prospective characteristics such as lowpower consumption, high sensitivity, high switching speed, high packet density, etc. Somuch attention has been attracted on their fabrication and industrial realization.

(a) (b)Fig. 1 a) schematic diagram of SET b) a schematic circuit of SET[9]

2 Fabrication of SETBut the fabrication of SET promotes many difficulties. For SET to be used in a largescale industrially, these factors must be considered:

• It's vitally important to develop technologies for forming nanoscale QDs andquantum wires, which are coupled together through tunneling barrier, and whichmust be precisely controlled in their size and position.

• Process induced damage and contamination must be avoided in the fabrication oflarge scale SET circuits.

• The technique must have high reproducibility and controllability.Basically the fabrication methods can be divided as physical or chemical techniquesaccording to the main procedures.The physical methods often utilize the combination of thin film and lithographictechnologies. Devices with carefully tailored geometries and electron density are got. Forexample, quantum dots or quasi-zero-dimensional puddles of electrons with weakcoupling to simultaneously patterned electrical leads are fabricated to form a SET.However, lithographic and materials limitations restrict the minimum size andcomposition of such dots (100nm), and studies are typically limited to sub-Kelvintemperatures.

Another approach is to grow nanostructures chemically. [1,2]This approach is prosperousfor its low cost and good controllability of the size of Coulomb islands, and it is possibleto be a prospective technique. Though this technique is not mature industrially, the SETsfabricated in laboratories show fascinating results. Generally there are three most

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important steps: first, the fabrication of Coulomb islands as well as the control of theirsize and dispersity; second, the formation of tunneling junctions at the joint of electrodesand Coulomb island; third, the formation of gate between substrate and Coulomb islands.The picture below is an example. First, an insulating layer (SiO2) 100nm thick is formedon the Si substrate (or TiO2 on 32OAl−α ), then Au leads are arranged on the substrate

by optical lithography coupled with shadow evaporation. Nanocrystals are then attachedto the Au leads via a bifunctional linker molecule, forming the Coulomb islands. Thenanocrystals used by Klein etc. are Au and CdSe of 5.8nm in diameter. Figure 2 showsthe curve they got for measured current I and source-drain bias Vsd at 77K. A coulombstaircase is observed, due to the incremental charging of the dot by single electrons withincreasing Vsd, which is characteristic for SET.

Fig. 2 a) Field emission scanning electron micrograph of a lead structure beforenanocrystals are introduced. The light gray region (10nm) is formed by the angleevaporation, the darker region (70nm) is from a normal angle evaporation. b) Schematiccross section of nanocrystals bound via a bifunctional linker molecule to the leads.d) I-Vsd characteristic of a 5.8nm diam Au nanocrystal measured at 77K.

Atomic force microscopy (AFM) nano-oxidation process [3]Yoshitaka etc. developed a method to use AFM to fabricate SET. 32OAl−α is used as

the substrate, a layer of Ti is deposit on the substrate. As a pulse bias is applied betweenthe SFM top and the surface of Ti metal film, the moisture in the ambient air isdecomposed and a TiOx line of 15~25nm is formed by chemical reaction. These lineswork as the tunnel junctions. The fabricated SET consists of one island sandwiched

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between two tunnel junctions. The island width is about 8nm. Typical Coulomboscillation is observed in this SET, with the period about 2V.The advantage of AFM is the controllability of size and position in the viewpoint ofnanofabrication. But the shortage of this method is it is not so suitable for fabricatinglarge quantities.

In order to optimize the device properties, the reproducible structure of Si-based SETs aresubstantially studied. Its advantage is that the size of Si islands can be geometrically wellcontrolled because of the advance of modern semiconducting technologies. A side-wallpatterning method is proposed. This is based on a silicon-on-insulator (SOI) quantumwire and an electrostatically defined island beyond the limit of lithography resolution.This method takes the advantage of the good selectivity in reactive-ion plasma betweenSi and SiO2, and finally a 30nm-wide quantum wire is formed, and then poly-Si sidewalldepletion gate is formed between these wires, this depletion areas work as Coulomislands. The characteristic I-V curve is observed for this system. This method is veryprospective for the possibility of large scale of fabricating SETs.[15]

Fig. 3[4] Schematics of the process sequence of side-wall patterning method

3 ApplicationsBecause of its small size, low energy consumption and high sensitivity, SET has foundmany applications in many areas. What's most exciting is the potential to fabricate themin large scale and use them as common units in modern computer and electronic industry.

Single electron memory[11]Scientists have long been endeavored to enhance the capacity of memory devices. Ifsingle electron memory can be realized, the memory capacity is possible to reach itsutmost limit. SET can be used as memory cell since the state of Coulomb island can bechanged by the existence of one electron. Chou and Chan [5] first pointed out thepossibility of using SET as memories in which information is stored as the presence orabsence of a single electron on the cluster. They fabricated a SET by embedding one orseveral nano Si powder in a thin insulating layer of SiO2, then arranging the source anddrain as well as gate around this Coulomb island. The read/write time of Chan's structureis about 20ns, lifetime is more than 109 cycles, and retention time (during which theelectron trapped in the island will not leak out) can be several days to several weeks.These parameters would satisfy the standards of computer industry, so SET can be

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developed to be a candidate of basic computer units. If a SET stands for one bit, then anarray of 4~7 SETs will be substantial to memorize different states. The properties of thememory unit composed of SETs are far more advantageous than that of CMOS. But thedisadvantage is the practical difficulty in fabrication. When the time comes for the largescale integration of SETs to form logic gates, the full advantages of single electronmemory will show. This is the threshold of quantum computing.

High sensitivity electrometerThe most advanced practical application currently for SETs is probably the extremelyprecise solid-state electrometers (a device used to measure charge). The SET electrometeris operated by capacitively coupling the external charge source to be measued to the gate.Changes in the SET source-drain current are then measured. Since the amplificationcoefficient is very big, this device can be used to measure very small change of current.Experiments showed that if there is a charge change of e/2 on the gate, the currentthrough the Coulomb island is about 109 e/sec. This sensitivity is many orders ofmagnitude better than common electrometers made by MOSFIT. SETs have already beenused in metrological applications as well as a tool for imaging localized individualchanges in semiconductors. Recent demonstration of single photon detection [6] and rfoperation [7] of SETs make them exciting for new applications ranging from astronomyto quantum computer read-out circuitry.The SET electrometer is in principle not limited to the detection of charge sites on asurface, but can also be applicable to a wide range of sensitive chemical signaltransduction events as well. For example, the gate can be made coupling with somemolecules, thus can measure other chemical properties during the process.

However, as Lewis K M etc. pointed out [8], SETs electrometer must be designed withcare. If the device under test has a large capacitance, it is not advantageous to use SETsas an electrometer. Since for a typical SET, FCSET µ1< , the suppression factor becomes

unacceptable when the macroscopic device has a capacitance in the pF or nF range.Therefore, SET amplifiers are not currently used for measuring real macroscopic devices.Other low-capacitance electrometers such as a recently proposed quantum point contactelectrometer also suffer from a similar capacitance mismatch problem. But it is believedthat if the capacitance mismatch can be solved efficiently, SETs may find many new ultralow-noise analog applications.

Microwave detectionIf a SET is attacked black body radiation, the photon-aided tunneling will affect thecharge transfer of the system. Experiments show that the electric character of the systemwill be changed even by a tiny amount of radiation. The sensitivity of this equipment isabout 100 times higher than the current best thermal radiation detector.

4 Main problems facing the application of SETa Integration of SETs in a large scaleAs has been mention above, to use SETs at room temperature, large quantities ofmonodispersed nanoparticles less than 10nm in diameter must be synthesized. it is very

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hard to fabricate large quantities of SETs by traditional optical lithography andsemiconducting process. Chemical self-assembly has the potential to solve this problem.This method adopts the metal-organic precursors and deposits nano clusters on thesubstrate. But the position cannot be decisively control and it's not a mature technology.The large quantity integration of SETs depends greatly on the development ofsemiconducting industry of nanotech.

b Linking SETs with the outside environmentMethods must be developed for connecting the individual structures into patterns whichfunction as logic circuits, and these circuits must be arranged into larger 2D patterns.There are two ideas. One is by doping, that is, integrating SET as well as relatedequipments with the existed MOSFIT, this is attractive because it can increase theintegrating density. The other is to give up linking by wire, instead utilizing the staticelectronic force between the basic clusters to form a circuit linked by clusters, which iscalled quantum cellular automata (QCA). Many have tried to use carbon nanotube[12] asleads between a serial of insulating nanoclausters. The state of "0" and "1" can be givenby polarization direction affected by applied voltage. Complex analog circuits can bemade by QCA. The advantage of QCA is its fast information transfer velocity betweencells (almost near optic velocity) via electrostatic interactions only, no wire is neededbetween arrays and the size of each cell can be as small as 2.5nm, this made them verysuitable for high density memory and the next generation quantum computer.

Fig. 4 Nanoparticle–insulator structures proposed in the wireless computing schemes ofKorotkov (top) and Lent (bottom). The circles represent quantum dots, the lines areinsulating spacers.[5]

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